Simplify ( square root of 36x^6)/( square root of 9x^4)

$\frac{\sqrt{36 x^{6}}}{\sqrt{9 x^{4}}}$

Combine $\sqrt{36 x^{6}}$ and $\sqrt{9 x^{4}}$ into a single radical.

$\sqrt{\frac{36 x^{6}}{9 x^{4}}}$

Reduce the expression $\frac{36 x^{6}}{9 x^{4}}$ by cancelling the common factors.

Factor $9$ out of $36 x^{6}$ .

$\sqrt{\frac{9 (4 x^{6})}{9 x^{4}}}$

Factor $9$ out of $9 x^{4}$ .

$\sqrt{\frac{9 (4 x^{6})}{9 (x^{4})}}$

Cancel the common factor.

$\sqrt{\frac{9 (4 x^{6})}{9 x^{4}}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{6}}{x^{4}}}$

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $4 x^{6}$ .

$\sqrt{\frac{x^{4} (4 x^{2})}{x^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{4} (4 x^{2})}{x^{4} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{4} (4 x^{2})}{x^{4} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{2}}{1}}$

Divide $4 x^{2}$ by $1$ .

$\sqrt{4 x^{2}}$

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\sqrt{{(2 x)}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$2 x$